A Compact Imbedding Theorem for Functions without Compact Support
R. A. Adams, John J. F. Fournier · Canadian Mathematical Bulletin · 1971
The extension of the Rellich-Kondrachov theorem on the complete continuity of Sobolev space imbeddings of the sort 1 to unbounded domains G has recently been under study [1–5] and this study has yielded [4] a condition on G which is necessary and sufficient for the compactness of (1). Similar compactness theorems for the imbeddings 2 are well known for bounded domains G with suitably regular boundaries, and the question naturally arises whether any extensions to unbounded domains can be made in this case.